Afi r s ti m p r e s s i o n
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1.4. Exercises on chapter 1
(1.1) Mixing
A water mass A, with a temperature T A =5 ◦ C and a salinity S A =3 5 .5 ppt,
is mixed with a water mass B, with a temperature T B =2 ◦ C and a salinity
S B =34.5 ppt. The resulting water has a temperature of 3 ◦ C and a salinity of
34.85 ppt.
a. Calculate the volume ratio of the water masses A and B in the mixture.
b. How can one determine this ratio graphically using a T -S diagram?
(1.2) Potential temperature
Consider in the table below some in-situ measurements of the temperature and
salinity at a certain location in the Atlantic.
Depth(m) Temperature ( ◦ C) Salinity (ppt)
0
18.909
32.574
1000
2.697
34.410
2000
1.868
34.600
3000
1.528
34.661
4000
1.456
34.679
5000
1.503
34.686
5460
1.547
34.688
a. Investigate whether the water column is statically stable when a linear
equation of state is assumed (with α T =10 −4 K −1 and α S =7.6 × 10 −4 ).
b. Why is the pressure dependence in the equation of state here important?
c. Determine the potential temperature as a function of depth for these
measurements.
d. Is the water column statically stable?
A water parcel with an in-situ temperature of T =1 0 ◦ C and a salinity of
S =3 5ppt moves adiabatically and without salinity changes from a depth of